A bilingual book is a story to share, not a promise of fluency. The research gives us some useful clues about language learning. It does not tell us that buying a book will make a child bilingual.
In a 2012 study, Erika Hoff and her colleagues followed two groups of toddlers from 22 to 30 months. One group of 47 was bilingual in Spanish and English, and the other 56 heard only English. Both groups came from families with high levels of education. The bilingual children scored lower when each language was counted alone. But their vocabulary totals across both languages were comparable to the English-only group's totals.
Within that bilingual group, hearing more of a language was linked to stronger vocabulary and grammar in that language. This was a study of language exposure, not a test of bilingual books. It did not show that reading Spanish first works better than reading English first.